Equity trading volume and volatility: An investigation of fractional integration and cointegration

Chapter 1 examines the behavior of equity trading volume and volatility for the individual firms comprising the Standard & Poors' 100 composite index. Using multivariate spectral methods, we find that fractionally integrated processes best describe the long-run temporal dependencies in both series. Consistent with a stylized Mixture of Distributions Hypothesis (MDH) model where the aggregate “news” arrival process possesses long-memory characteristics, the long-run hyperbolic decay rates appear to be common across each volume-volatility pair.; Chapter 2 examines the long-run behavior of individual equity trading volume and volatility for the individual firms comprising the Standard and Poors' 100 composite index and finds that the cross-correlations between trading volume and volatility decay at a hyperbolic rate, which is consistent with a modified Mixture of Distributions Hypothesis (MDH) model where a single latent information arrival process possesses fractionally integrated characteristics. We do not find such behavior in a model where two independent information arrival processes drive trading volume and volatility. A semiparametric two stage, residual based fractional cointegration test is applied to the volume and volatility series, and evidence is found to support the hypothesis that the series are fractionally cointegrated.; Chapter 3 examines the behavior of individual equity trading volatility for 93 firms continuously listed on the CRSP database for the 1962 to 1997 time period, and finds that mean reverting fractionally integrated processes best describe the long-run volatility dynamics of the overwhelming majority of these series. Adding measures of trading volume and volatility to the parametric specification reduces, but does not eliminate the estimated degree of volatility persistence. Equally significant results are found when the full sample period is decomposed into 3 sub-periods: 1962–1973, 1974–1985, and 1986–1997. A further panel data analysis of the 93 firms reveals that the degree of fractional integration for an individual equity series is related to both firm size and leverage factors.